Solve Q10, 11 explaining detailly each step dy aid in Advanced level Mathematics...42. The x-coordinate of the centriod of the area of the region defined by 02 y2 N(X-1) I8A. 1B.유 C.2D.13. The region bounded by the curve y= x+ 4 the lines y 8 and x 0 is rotated through 2nradians about the x-axis. The y coordinate of the centriod of the solid formed is:A. 0B.C.D.20. DIFFERENTIAL EQUATIONS1. The equation of a curve which passes through the point (2, 1) and has gradient 2x-5 is:A. y=-5x+5 B. y=x-5x-4 C. y=+ y-1D. y x -5x + 52. If1 =dx3-S then y=A. x- In(3-5x) +k B. In(3-5x) + kC. 1- 5ln(3-5x) +k D.25+ k(3-5x)3. The general solution of the differential equationdu+1=u wherek is a constant is:dtA. u =t+kB. u=t+1+k C.u I+kt D. u 1-kt4. Given thatdydxy+1and that y = 1 when x = 0, thenr+1A. y - 2x+3B. y = 2x +15. Given that 2 + x*y=x* and that y = 0 when x= 0, expressed in terms of x. y=C. y = 2xD. 2y = x+ 1A.B. 1+ e*C. 1-eD. 1-e*-6. The general solution of the differential equation1 dy= In x isA. y = (In x) + k B. y =;+ Inx)+kC.y=(-+ in x) +k D. y = 2 In x + k7. The general solution of the differential equation:dy2x +2xy, where k is a constant is:dxA. y= e*+k - 1 B. y e*+k-1 C. y e+k+ 1 D. y= e+k8. Ifu= 2 when x= 2, the particular solution of the differential equation ()= 1 is:dxA. u = x- In(x - 1)C. u =1+ In(x - 1)B. u=x + In(x-1)D.u x+ In(x - 1)+29. If (x+ 1) = 1-y and y = -3 when x 0 then y =A.B. -3C. 4x +3D. 4-4xx+110. Given that 2y- sin 2x = 0 and y = 0 when x 0, then y? =A.+ cos 2x11. The general solution of the differential equation cosy =positive constant is:A. Y=sin'x12. Given that y 1 when x = 2 the solution of the differential equation:(x - x) -v is1-cos 2xC-2 cos 2xcos 2xD.dy1siny where k is adxB. y= sin (kx)+:Cy= sin (1- kx) D. y sin (kx+1)dx51

Question

Accepted Answer

Answered: Image /qna-images/answer/8935e825-fbb1-4265-a131-2b8199086c06.jpg

10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A. D.-cos 2x Cos 2x 11 T. luti dy